Mathematical Model of COVID-19 with the Influence of Vaccination

Ndaru Atmi Purnami; Luqman Nuradi Prawadika; Irvandi Gorby Pasangka; Findasari Findasari; Eka Kusumawati; Ilham Yoga Pratama; Ridho Suharis; Nadhira Hasna Maturbongs

doi:10.37905/euler.v13i3.34182

Mathematical Model of COVID-19 with the Influence of Vaccination

Ndaru Atmi Purnami, Luqman Nuradi Prawadika, Irvandi Gorby Pasangka, Findasari Findasari, Eka Kusumawati, Ilham Yoga Pratama, Ridho Suharis, Nadhira Hasna Maturbongs

Abstract

The COVID-19 pandemic, which first emerged at the end of 2019, has had a significant impact on people's lives around the world. In Indonesia, the outbreak began to develop in February 2020. Although the pandemic has now passed and people have started to resume their normal activities, some individuals are still being infected with COVID-19, even though the number of cases is now under control. One of the key factors in controlling COVID-19 is vaccination. The extent to which vaccination affects COVID-19 transmission will be discussed in this study. Furthermore, a numerical simulation will be conducted on this mathematical model to observe the impact of vaccination on COVID-19. The mathematical model of COVID-19 with vaccination influence will describe the interaction between six population classes, namely: the class of susceptible individuals who can be infected (Susceptible – S), the class of exposed individuals (Exposed – E), the class of vaccinated individuals who have never been infected (Vaccinated – V), the class of infected individuals (Infected – I), the class of individuals who have recovered (Recovered – R), and the class of infected individuals who have died (Death – D). It is important to note that COVID-19 is a disease caused by infection with the coronavirus. A person who has not yet been infected with the virus has the potential to be exposed. One way to prevent exposure is through vaccination. In Indonesia, vaccination has been made mandatory three times: the first dose, the second dose, and the booster. However, because the coronavirus has an incubation period, there is no guarantee that a vaccinated person has not already been exposed to the virus. Exposed individuals will become infected with COVID-19 once the incubation period ends. Infected individuals may show symptoms or be asymptomatic. An infected individual has two possible outcomes: recovery or death. The modeling is based on the SEVIRD model, with its parameters estimated using data. This study produces a mathematical model of COVID-19 with vaccination influence, showing that vaccination plays a role in controlling the spread of COVID-19.

Keywords

COVID-19; SEVIRD; Coronavirus; Vaccination; Mathematical Modeling.

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DOI: https://doi.org/10.37905/euler.v13i3.34182